The Biot-Cosserat Continuum Model For Unsaturated Soil And Finite Element Simulation

The unsaturated soil is modeled as a multiphase porous medium consisting of the solid skeleton constructed with soil particles and voids filled with pore water and air. It widely exists in the nature and engineering practices. The study of its coupled hydro-mechanical behaviors is of great scientific significance to tackle geotechnical problems such as the slope stability problem subjected to flood or rainstorm loads(including debris flow and landslide), the subsidence of soil foundation in the excavation process of tunnels, and consequently to further develop the system of forecasting and preventing the geological disasters.Based on the classical Cauchy unsaturated porous continuum, the independent rotation degree of freedom and micro-curvatures as its spatial derivatives, the coupled stresses energetically conjugated to the micro-curvatures for solid phase are introduced to the Cosserat unsaturated porous continuum. In light of mass and momentum (moment of momentum) conservation laws for the three phases in unsaturated soils, i.e. the solid skeleton, the pore water and the pore air, the governing equations for unsaturated porous Biot-Cosserat continuum model are derived by means of the combination of both Cosserat continuum theory and Biot theory with abandoning the passive air phase assumption. The finite element formulations governing the coupled hydro-dynamic behavior with the primary variables of the displacements and the microrotation for the solid phase and pressures for the pore water and air are derived on the basis of the Galerkin-weighted residual method and Newmark method for the spatial and temporal discretizations, respectively.As the numerical simulation of coupled hydro-dynamic process in unsaturated soil is concerned, in order to prevent the spurious oscillations in spatial domain that may occur in the pressure field, caused by the equal low order interpolation function spaces in the mixed finite element formulation with the n(ω)-pw-pa form, the unequal order interpolation functions are used in this paper. The bi-quadratic quadrilateral elements are used for the displacements and microrotation while the bi-linear quadrilateral elements are chosen for the pore water and pore air pressure. Numerical results illustrate the capability of the developed model and the finite element method for the coupled hydro-dynamic process in unsaturated porous media.